feat: add support for accessor arrays and refactor stats/base/variancetk

lib/node_modules/@stdlib/stats/base/variancetk/README.md

@@ -98,9 +98,9 @@ The use of the term `n-1` is commonly referred to as Bessel's correction. Note,
 var variancetk = require( '@stdlib/stats/base/variancetk' );
 ```
 
-#### variancetk( N, correction, x, stride )
+#### variancetk( N, correction, x, strideX )
 
-Computes the [variance][variance] of a strided array `x` using a one-pass textbook algorithm.
+Computes the [variance][variance] of a strided array using a one-pass textbook algorithm.
 
 ```javascript
 var x = [ 1.0, -2.0, 2.0 ];
@@ -114,17 +114,14 @@ The function has the following parameters:
 -   **N**: number of indexed elements.
 -   **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
 -   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
--   **stride**: index increment for `x`.
+-   **strideX**: stride length for `x`.
 
-The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`,
+The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`,
 
 ```javascript
-var floor = require( '@stdlib/math/base/special/floor' );
-
 var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
-var N = floor( x.length / 2 );
 
-var v = variancetk( N, 1, x, 2 );
+var v = variancetk( 4, 1, x, 2 );
 // returns 6.25
 ```
 
@@ -134,18 +131,15 @@ Note that indexing is relative to the first index. To introduce an offset, use [
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
-var floor = require( '@stdlib/math/base/special/floor' );
 
 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
 
-var N = floor( x0.length / 2 );
-
-var v = variancetk( N, 1, x1, 2 );
+var v = variancetk( 4, 1, x1, 2 );
 // returns 6.25
 ```
 
-#### variancetk.ndarray( N, correction, x, stride, offset )
+#### variancetk.ndarray( N, correction, x, strideX, offsetX )
 
 Computes the [variance][variance] of a strided array using a one-pass textbook algorithm and alternative indexing semantics.
 
@@ -158,17 +152,14 @@ var v = variancetk.ndarray( x.length, 1, x, 1, 0 );
 
 The function has the following additional parameters:
 
--   **offset**: starting index for `x`.
+-   **offsetX**: starting index for `x`.
 
-While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [variance][variance] for every other value in `x` starting from the second value
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the [variance][variance] for every other element in the strided array starting from the second element
 
 ```javascript
-var floor = require( '@stdlib/math/base/special/floor' );
-
 var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
-var N = floor( x.length / 2 );
 
-var v = variancetk.ndarray( N, 1, x, 2, 1 );
+var v = variancetk.ndarray( 4, 1, x, 2, 1 );
 // returns 6.25
 ```
 
@@ -181,6 +172,7 @@ var v = variancetk.ndarray( N, 1, x, 2, 1 );
 ## Notes
 
 -   If `N <= 0`, both functions return `NaN`.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
 -   If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.
 -   Some caution should be exercised when using the one-pass textbook algorithm. Literature overwhelmingly discourages the algorithm's use for two reasons: 1) the lack of safeguards against underflow and overflow and 2) the risk of catastrophic cancellation when subtracting the two sums if the sums are large and the variance small. These concerns have merit; however, the one-pass textbook algorithm should not be dismissed outright. For data distributions with a moderately large standard deviation to mean ratio (i.e., **coefficient of variation**), the one-pass textbook algorithm may be acceptable, especially when performance is paramount and some precision loss is acceptable (including a risk of returning a negative variance due to floating-point rounding errors!). In short, no single "best" algorithm for computing the variance exists. The "best" algorithm depends on the underlying data distribution, your performance requirements, and your minimum precision requirements. When evaluating which algorithm to use, consider the relative pros and cons, and choose the algorithm which best serves your needs.
 -   Depending on the environment, the typed versions ([`dvariancetk`][@stdlib/stats/strided/dvariancetk], [`svariancetk`][@stdlib/stats/strided/svariancetk], etc.) are likely to be significantly more performant.
@@ -196,18 +188,12 @@ var v = variancetk.ndarray( N, 1, x, 2, 1 );
 <!-- eslint no-undef: "error" -->
 
 ```javascript
-var randu = require( '@stdlib/random/base/randu' );
-var round = require( '@stdlib/math/base/special/round' );
-var Float64Array = require( '@stdlib/array/float64' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
 var variancetk = require( '@stdlib/stats/base/variancetk' );
 
-var x;
-var i;
-
-x = new Float64Array( 10 );
-for ( i = 0; i < x.length; i++ ) {
-    x[ i ] = round( (randu()*100.0) - 50.0 );
-}
+var x = discreteUniform( 10, -50, 50, {
+    'dtype': 'float64'
+});
 console.log( x );
 
 var v = variancetk( x.length, 1, x, 1 );
@@ -257,6 +243,8 @@ console.log( v );
 
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
 [@stdlib/stats/strided/svariancetk]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/svariancetk
 
 [@ling:1974a]: https://doi.org/10.2307/2286154

lib/node_modules/@stdlib/stats/base/variancetk/benchmark/benchmark.js

@@ -21,11 +21,18 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var pkg = require( './../package.json' ).name;
-var variancetk = require( './../lib/variancetk.js' );
+var variancetk = require( './../lib/main.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
 
 
 // FUNCTIONS //
@@ -38,13 +45,7 @@ var variancetk = require( './../lib/variancetk.js' );
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = [];
-	for ( i = 0; i < len; i++ ) {
-		x.push( ( randu()*20.0 ) - 10.0 );
-	}
+	var x = uniform( len, -10, 10, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/variancetk/benchmark/benchmark.ndarray.js

@@ -21,13 +21,20 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var pkg = require( './../package.json' ).name;
 var variancetk = require( './../lib/ndarray.js' );
 
 
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
 // FUNCTIONS //
 
 /**
@@ -38,13 +45,7 @@ var variancetk = require( './../lib/ndarray.js' );
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = [];
-	for ( i = 0; i < len; i++ ) {
-		x.push( ( randu()*20.0 ) - 10.0 );
-	}
+	var x = uniform( len, -10, 10, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/variancetk/docs/repl.txt

@@ -1,10 +1,10 @@
 
-{{alias}}( N, correction, x, stride )
+{{alias}}( N, correction, x, strideX )
     Computes the variance of a strided array using a one-pass textbook
     algorithm.
 
-    The `N` and `stride` parameters determine which elements in `x` are accessed
-    at runtime.
+    The `N` and stride parameters determine which elements in the strided array
+    are accessed at runtime.
 
     Indexing is relative to the first index. To introduce an offset, use a typed
     array view.
@@ -31,8 +31,8 @@
     x: Array<number>|TypedArray
         Input array.
 
-    stride: integer
-        Index increment.
+    strideX: integer
+        Stride length.
 
     Returns
     -------
@@ -46,22 +46,19 @@
     > {{alias}}( x.length, 1, x, 1 )
     ~4.3333
 
-    // Using `N` and `stride` parameters:
+    // Using `N` and stride parameters:
     > x = [ -2.0, 1.0, 1.0, -5.0, 2.0, -1.0 ];
-    > var N = {{alias:@stdlib/math/base/special/floor}}( x.length / 2 );
-    > var stride = 2;
-    > {{alias}}( N, 1, x, stride )
+    > {{alias}}( 3, 1, x, 2 )
     ~4.3333
 
     // Using view offsets:
     > var x0 = new {{alias:@stdlib/array/float64}}( [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ] );
     > var x1 = new {{alias:@stdlib/array/float64}}( x0.buffer, x0.BYTES_PER_ELEMENT*1 );
-    > N = {{alias:@stdlib/math/base/special/floor}}( x0.length / 2 );
-    > stride = 2;
-    > {{alias}}( N, 1, x1, stride )
+    > {{alias}}( 3, 1, x1, 2 )
     ~4.3333
 
-{{alias}}.ndarray( N, correction, x, stride, offset )
+
+{{alias}}.ndarray( N, correction, x, strideX, offsetX )
     Computes the variance of a strided array using a one-pass textbook algorithm
     and alternative indexing semantics.
 
@@ -89,10 +86,10 @@
     x: Array<number>|TypedArray
         Input array.
 
-    stride: integer
-        Index increment.
+    strideX: integer
+        Stride length.
 
-    offset: integer
+    offsetX: integer
         Starting index.
 
     Returns
@@ -108,9 +105,8 @@
     ~4.3333
 
     // Using offset parameter:
-    > var x = [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ];
-    > var N = {{alias:@stdlib/math/base/special/floor}}( x.length / 2 );
-    > {{alias}}.ndarray( N, 1, x, 2, 1 )
+    > x = [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ];
+    > {{alias}}.ndarray( 3, 1, x, 2, 1 )
     ~4.3333
 
     See Also

lib/node_modules/@stdlib/stats/base/variancetk/docs/types/index.d.ts

@@ -20,7 +20,12 @@
 
 /// <reference types="@stdlib/types"/>
 
-import { NumericArray } from '@stdlib/types/array';
+import { NumericArray, Collection, AccessorArrayLike } from '@stdlib/types/array';
+
+/**
+* Input array.
+*/
+type InputArray = NumericArray | Collection<number> | AccessorArrayLike<number>;
 
 /**
 * Interface describing `variancetk`.
@@ -32,7 +37,7 @@ interface Routine {
 	* @param N - number of indexed elements
 	* @param correction - degrees of freedom adjustment
 	* @param x - input array
-	* @param stride - stride length
+	* @param strideX - stride length
 	* @returns variance
 	*
 	* @example
@@ -41,16 +46,16 @@ interface Routine {
 	* var v = variancetk( x.length, 1, x, 1 );
 	* // returns ~4.3333
 	*/
-	( N: number, correction: number, x: NumericArray, stride: number ): number;
+	( N: number, correction: number, x: InputArray, strideX: number ): number;
 
 	/**
 	* Computes the variance of a strided array using a one-pass textbook algorithm and alternative indexing semantics.
 	*
 	* @param N - number of indexed elements
 	* @param correction - degrees of freedom adjustment
 	* @param x - input array
-	* @param stride - stride length
-	* @param offset - starting index
+	* @param strideX - stride length
+	* @param offsetX - starting index
 	* @returns variance
 	*
 	* @example
@@ -59,7 +64,7 @@ interface Routine {
 	* var v = variancetk.ndarray( x.length, 1, x, 1, 0 );
 	* // returns ~4.3333
 	*/
-	ndarray( N: number, correction: number, x: NumericArray, stride: number, offset: number ): number;
+	ndarray( N: number, correction: number, x: InputArray, strideX: number, offsetX: number ): number;
 }
 
 /**
@@ -68,7 +73,7 @@ interface Routine {
 * @param N - number of indexed elements
 * @param correction - degrees of freedom adjustment
 * @param x - input array
-* @param stride - stride length
+* @param strideX - stride length
 * @returns variance
 *
 * @example

lib/node_modules/@stdlib/stats/base/variancetk/docs/types/test.ts

@@ -16,6 +16,7 @@
 * limitations under the License.
 */
 
+import AccessorArray = require( '@stdlib/array/base/accessor' );
 import variancetk = require( './index' );
 
 
@@ -26,6 +27,7 @@ import variancetk = require( './index' );
 	const x = new Float64Array( 10 );
 
 	variancetk( x.length, 1, x, 1 ); // $ExpectType number
+	variancetk( x.length, 1, new AccessorArray( x ), 1 ); // $ExpectType number
 }
 
 // The compiler throws an error if the function is provided a first argument which is not a number...
@@ -101,6 +103,7 @@ import variancetk = require( './index' );
 	const x = new Float64Array( 10 );
 
 	variancetk.ndarray( x.length, 1, x, 1, 0 ); // $ExpectType number
+	variancetk.ndarray( x.length, 1, new AccessorArray( x ), 1, 0 ); // $ExpectType number
 }
 
 // The compiler throws an error if the `ndarray` method is provided a first argument which is not a number...

lib/node_modules/@stdlib/stats/base/variancetk/examples/index.js

@@ -18,18 +18,12 @@
 
 'use strict';
 
-var randu = require( '@stdlib/random/base/randu' );
-var round = require( '@stdlib/math/base/special/round' );
-var Float64Array = require( '@stdlib/array/float64' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
 var variancetk = require( './../lib' );
 
-var x;
-var i;
-
-x = new Float64Array( 10 );
-for ( i = 0; i < x.length; i++ ) {
-	x[ i ] = round( (randu()*100.0) - 50.0 );
-}
+var x = discreteUniform( 10, -50, 50, {
+	'dtype': 'float64'
+});
 console.log( x );
 
 var v = variancetk( x.length, 1, x, 1 );